Simulating composite fermion excitons on a disk by density functional theory and Monte Carlo

The Kohn-Sham density functional method for the fractional quantum Hall (FQH) effect has recently been developed by mapping the strongly interacting electrons into an auxiliary system of weakly interacting composite fermions (CFs) that experience a density-dependent effective magnetic field. This approach has been successfully applied to explore the edge reconstruction, fractional charge, and fractional braiding statistics of quasiparticle excitations. In this work, we investigate composite fermion excitons in the bulk of the disk geometry. By varying the separation of the quasiparticle-quasihole pairs and calculating their energy, we compare the dispersion of the exciton with results from other numerical methods, such as exact diagonalization (ED) and Monte Carlo (MC) simulation. Furthermore, from the spectral function calculation, we identify chiral ``graviton'' excitations: a spin $\ensuremath{-}2$ mode for the particle-like Laughlin state and a spin 2 mode for the hole-like Laughlin state. This method can be extended to construct neutral collective excitations for other fractional quantum Hall states in disk geometry.